A novel PDE based image restoration: Convection–diffusion equation for image denoising

In this paper we present a convection–diffusion equation for processing image denoising, edge preservation and compression. We compare it with a popular nonlinear diffusion model which has been widely implemented in image denoising for Gaussian white noise. Here we show that this convection–diffusion model effectively removes noise, especially for the mixture of Gaussian and salt-and-pepper noises. We propose the modified streamline diffusion method [Y. Shih, H.C. Elman, Modified streamline diffusion schemes for convection–diffusion problems, Comput. Methods Appl. Mech. Eng, 1998.] for the discretization of this convection–diffusion model to prevent internal layers because of the discontinuities while using the coarsening algorithm for the image compression. Numerical experiments have shown that our convection–diffusion model for removing both Gaussian and salt-and-pepper noises, efficiently and reliably preserves edges quite satisfactorily.